Low frequency equalization for loudspeaker system

ABSTRACT

A method of optimizing the low frequency audio response emanating from a pair of low frequency transducers housed within a cabinet. The low frequency transducers are electrically connected to a power amplifier and source of audio content. The resonant frequency (Fs) and amplitude (Q) are characterized as to the high-pass pole of the low frequency transducers as they are mounted within the cabinet. An equalizer is placed between the amplifier and source of audio content for canceling the complex pole of the low frequency transducers and for establishing a new complex pole at a cut off frequency below which the sound generated by the low frequency transducers will diminish.

This application is a continuation of U.S. patent application Ser. No.11/708,406, filed Feb. 20, 2007, now issued as U.S. Pat. No. 8,098,849,which is a continuation-in-part application of U.S. patent applicationSer. No. 11/324,650, filed Jan. 3, 2006 now abandoned, and is entitledto those filing dates for priority in whole or in part. Thespecification, figures and complete disclosure of U.S. patentapplication Ser. Nos. 11/708,406 and 11/324,650 are incorporated hereinby specific reference for all purposes.

FIELD OF INVENTION

The present invention involves a method of optimizing the low frequencyaudio response emanating from a pair of low frequency transducers housedwithin a cabinet. When the proper equalization circuit is installedwithin the audio chain, the woofer portion of a speaker system can beoptimized to an extent not previously achievable.

BACKGROUND OF THE INVENTION

Loudspeaker systems including those intended for residential two channelaudio or multi-channel theater systems intend to embrace a substantialportion of the audio frequency range discernable by a listener. Animportant part of this range are low frequencies produced by relativelylarge loudspeaker transducers, generally known as woofers.

As with the mid and high-frequency parts of the audible range, it isknown that the correct reproduction of musical pitch and timbre isstrongly related to the attack part of the sound and less so to thedecay part. The low frequencies are important in this regard because inall of occidental music the harmony is built upon the bass. If thereproduction of the bass frequencies has a slow attack, the overallsound is perceived as having an uncertain sense of pitch and a poorsense of rhythmic drive. It is thus of very great importance to designwoofer systems which correctly render the attack part of the sound.

The correct rendering of the attack requires the ability for the motorof the loudspeaker to quickly accelerate the diaphragm. Sinceacceleration is proportional to force divided by mass it is necessarythat the woofer transducer has a light moving system and a powerfulmotor. Conventionally designed woofer systems generally embody theopposite of these requirements. This is because there is a universaldesire to make the woofer enclosure as small as possible. As will bediscussed below, the stiffness of the air in the enclosure adverselymodifies the characteristic of the woofer transducer, makingoptimization difficult at best and often impossible.

An excellent woofer system is shown schematically in FIG. 1. Woofersystem 10 is comprised of cabinet 11 housing low frequency transducers12 and 13. These low frequency transducers ideally operate in phase witheach other whereby diaphragms 14 and 15 face each other being driven bymotor assemblies 16 and 17. When low frequency transducers 12 and 13 aremounted opposite to one another as shown FIG. 1, large reaction forcesassociated with high power woofers located in cabinet structure 11 neednot rely on mechanical grounding of the cabinet to the surroundingstructures upon which the cabinet is placed.

In analyzing the low frequency transducer model of FIG. 1, one cancreate an electrical equivalent circuit (mobility analogy) of thisassembly in free air. This is shown in FIG. 2A as a second-orderresonant circuit with a natural frequency determined by the stiffness ofthe suspension and mass of the moving system. The amplitude (Q) of thisresonance is determined by the damping due to mechanical loss. Theresonance can be defined in terms of frequency and Q, and it constitutesa complex high-pass pole in the response of the loudspeaker.

Notwithstanding the above discussion, the electrical equivalent circuitshown in FIG. 2A does not tell the entire story. In this regard,reference is made to FIG. 2B. In this regard, when low frequencytransducers 12 and 13 are placed within cabinet 11 which can be, forexample, a sealed box, the stiffness of the air in the box is added tothe stiffness of the suspension of the low frequency transducers and isshown as a parallel inductor. The consequence of this is that both theresonant frequency and Q are raised in value by approximately the squareroot of (1+(the stiffness of the speaker divided by the stiffness of theair in the box)). This can graphically be depicted by comparing FIGS. 2Cand 2D.

A design goal of a woofer system is to maintain a low resonantfrequency. Traditionally, this was done by increasing the moving mass(diaphragms 14 and 15), decreasing diaphragm stiffness or both.Stiffness has traditionally been decreased by making suspensioncomponents employed in such transducers more flexible or “limp” or bymaking enclosure 11 larger. Again, moving mass can only be increased bymaking diaphragms 14 and 15 heavier. However, adopting any of thesetraditional expedients represent a significant compromise as they tendto degrade performance of the woofer system. Softer suspension parts arenot reliable, particularly if they are carrying a greater mass.Increased mass further requires a corresponding increase in motorstrength if the ability to accelerate diaphragms 14 and 15 is to bemaintained. A larger motor translates directly to higher productioncosts and a larger enclosure 11 may not be a suitable solution ascabinet size is generally considered to be a design constraint on anyloudspeaker system. As a result, those engaged in loudspeaker designgenerally simply choose appropriately sized low frequency transducers,enclose them in an available volume and accept the resulting response.

It is thus an object of the present invention to provide a noveltechnique for dealing with the resonance of a low frequency transducersystem.

It is yet a further object of the present invention to improve theoperating range of a woofer system by providing an electrical circuit asan equal within the audio chain.

These and further objects will be more readily apparent when consideringthe following disclosure and appended claims.

SUMMARY OF THE INVENTION

The present invention involves a method of optimizing the low frequencyaudio response emanating from a pair of low frequency transducers housedwithin a cabinet, said low frequency transducers being electricallyconnected to a power amplifier and source of audio content, said methodcomprises characterizing the resonant frequency (Fs) and amplitude (Q)of the high-pass pole of the low frequency transducers as they aremounted within said cabinet, placing an equalizer between said amplifierand source of audio content. Said equalizer canceling the complex poleof the low frequency transducers and establishing a new complex polethus establishing a new cut off point below which the low frequencysound will diminish. The topology of the equalizer permits independentvariation of the parameters which facilitates dynamic variation of saidparameters to continuously adapt the equalizer in order to preventexcessive excursion of the woofers.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a side cut away view of a typical woofer cabinet and enclosedlow frequency transducers which can be employed in benefiting from thepresent invention.

FIGS. 2A and 2B are electrical equivalent circuits of the wooferassembly of FIG. 1 in free air (FIG. 2A) and in a sealed cabinet (FIG.2B).

FIGS. 2C and 2D correspond to FIGS. 2A and 2B, respectively, showing agraphical equivalent of the relationship between the output or response(dB) and frequency of woofer systems.

FIG. 3 is a block diagram of the equalizer system made the subject ofthe present invention.

FIGS. 4A and 4B are schematic layouts and graphical depictions of theequalizer system shown in FIG. 3.

FIG. 5 is a graphical depiction of the relationship between wooferoutput (dB) and frequency showing the effect of the equalizer systemshown in FIGS. 3 and 4.

FIG. 6 is a block diagram of the equalizer with voltage-controllableadjustment of the equalization frequency ratio and control sidechain.

FIG. 7 is a schematic diagram of the variable equalizer.

FIG. 8 shows the effect of the variable adaptive equalization.

DETAILED DESCRIPTION OF THE INVENTION

The present design approach or method of optimizing low frequencytransducer response in a loudspeaker system bears little or no parallelto loudspeaker design methodology engaged in previously. In the past, adesigner would select what is believed to be properly sized anddimensioned transducers placed in what is hoped to be an appropriatelysized cabinet fed by low frequencies emanating from a power amplifierthrough an appropriate cross over network. In practicing the presentinvention, however, a designer could begin with a preconfigured woofersystem and by inserting the appropriate equalization circuit between thepower amplifier and the audio content source, this woofer system can beoptimized.

All woofer systems have a natural resonance or preferred naturalfrequency. In an electric circuit or an electric analogy to a mechanicalsystem, resonance occurs because of the exchange of energy between thereactive elements, i.e., capacitance and inductance, of the circuit. Itis recognized that the resistive elements of a circuit are dissipative,noting if there was no resistance in a circuit (which is obviously aphysical impossibility), the resonant exchange of energy or oscillationwould persist indefinitely. As resistance is introduced into this idealmodel, the quality of the resonance or its amplitude (Q) deteriorates.In the loudspeaker electrical analogy at hand, capacitance correspondsto mass, inductance corresponds to compliance and resistance correspondsto mechanical resistance Obviously, the opposite of Q is damping (d) sothat d=1/Q. As such, any single resonance can be characterized by itsfrequency and its Q (or d), the mathematical description of a resonantsystem can be described as follows where:S=jω+Ø

-   -   S=Complex frequency variable    -   j=square root of (−1), the complex operator    -   ω=2πf, where f is in Hz=¹/sqrt (mass×compliance)    -   Ø=Phase angle        The notation of this equation denotes a real and an imaginary        axis for S. When a resonant circuit is expressed in S, the roots        of the equation in the numerator represent “zeros” in the        “S-plane” and the roots of the denominator represent “poles” in        the S-plane. In solving the transfer function for a system with        both poles and zeros noting that not all systems have both, if        there are identical coefficients for a pole and a zero, they        cancel each other. A complex pole in S is a resonance and can be        described in terms of F and Q.

It is recognized herein that any speaker, by itself, has a fundamentalresonant frequency (Fs) related to the mass of the diaphragm or coneoscillating on the compliance of the transducer suspension. Thesharpness of this resonance is determined by the friction losses in theparts and by the electromagnetic drag from the motor which both drivesand brakes the diaphragm.

It is further recognized that if one places a transducer in a cabinet,the stiffness of whose air volume is significant, generallycharacterized by a relatively small cabinet, the radian frequency (ω)will increase because compliance decreases. The result is a new resonantfrequency for the complete system, denoted as Ftc, Qtc. It is a propertyof direct radiator loudspeakers that below their resonant frequency,response diminishes. For a closed-box system, the response fallsasymptotically to 12 dB/octave below the resonance. As such, if theresonance has been pushed up in frequency by a too-small box, the usefullow frequency response will be diminished.

These characteristics were previously discussed with regard to FIGS. 2Aand 2B and the corresponding FIGS. 2C and 2D. As to FIGS. 2A and 2C, thewoofer or low frequency transducer in free air shows that it is asecond-order resonant circuit with a natural frequency determined by thestiffness of the suspension and the mass of the moving system. Theamplitude of this resonance (Q) is determined by damping due tomechanical losses and, as noted above, is defined in terms of frequencyand Q as it constitutes a complex high-pass pole in the response of theloudspeaker. By contrast, as noted in reference to FIGS. 2B and 2D, thestiffness of the air in the box is added to the stiffness of thesuspension of the speaker shown as a parallel inductor. The consequenceof this is that both the resonant frequency and its Q are raised invalue by approximately the square root of (1+(the stiffness of thespeaker divided by the stiffness of air in the box)). Designers in thepast have attempted to keep resonant frequency low by increasing movingmass and decreasing stiffness of the transducer, or both. However, asnoted above, these design goals are difficult to achieve. By contrast,the present invention optimizes the transducers enclosed in an availablevolume by providing an equalizing circuit imposed between the source ofan audio signal and power amplifier used to drive the lowest frequencytransducers.

Although the equal g circuit will be described in detail hereinafter,broadly, it operates by 1) characterizing the enclosed woofer system asto its resonant frequency (Fs) and Q of its high-pass complex pole, 2)placing a matching complex zero in the signal path to cancel the speakercharacteristic and 3) establishing a new complex pole at an arbitrarilychosen low frequency which defines the new low frequency cut off of thewoofer system. This latter characteristic of the equalizing circuit isnecessary to prevent the woofer system from being overrun by largesignals below the intended operating range and may be made dynamicallyvariable to extend the dynamic range.

FIG. 3 provides a conceptual diagram of the equalizer of the presentinvention. This is a two integrator state-variable filter which istopologically well known in the art of filter design. The conjugateequalizer shown in FIG. 3 is illustrated schematically in FIG. 4. In theexample of FIG. 4, resistor values are normalized to 10.0 KΩ. Forexample R11=Q_(p) (F_(z)/F_(p))×10 K′Ω. The radian frequency (ω) equals2 πf so that, for example, given C1=C2=100 nF and given F_(z)=70 Hz,then R2=R3=22.74 K′Ω. The functions are U1 and U5 are inverting summingamplifiers. U2 and U3 are integrators. U4 is a unity-gain invertingamplifier. As such, Fz, Qz of the equalizer cancels the complex pole ofthe speaker denoted as Ftc, Qtc. The combined response then remains flatdown to Fp, Qp which is the new cut off frequency for the completesystem. There are simpler circuits which will accomplish the conjugateequalization, but the two-integrator state-variable filter has theadvantage that the four parameters of interest, Fz, Qz, Fp and Qp areindependently adjustable. This allows an improvement to be describedbelow.

Graphically, the effect of the equalizer circuit is shown in FIG. 5. Itis noted that the equalizer response creates a new pole while theresponse vs. frequency characterization of the speaker in its cabinetshifts as depicted in FIG. 5.

Because the entire arrangement substitutes amplifier power for movingmass (as a way of overcoming the increased stiffness), it is importantto recognize that the transducers must be constructed so as to withstandhigh power inputs at low frequencies. The rate of increase of responseof the equalizer with decreasing frequency is 12 dB/octave. Put anotherway, if the equalization extends from 70 Hz downward to 20 Hz (typicalvalues) then the required amplifier power at 20 Hz will be 21.7 dBgreater than at 70 Hz (in a Bode straight-line approximation). This is apower ratio of 148:1. This is not a problem because the previouslyoptimized woofers can have very high sensitivity. The elevatedsensitivity comes from the fact that the conversion efficiency isproportional to the resonant frequency cubed, and inversely proportionalto the stiffness.

There is a further advantage to this arrangement. In a conventionalwoofer system, the entire useful operating range is above thefundamental resonance of the enclosed system and is thereforemass-controlled. In a mass-controlled system, the acoustic output lagsthe electrical input by 90 degrees. At long wavelengths this issignificant because 90 degrees at 50 Hz is equivalent to a 5 footdistance, i.e., temporally the woofer is 5 feet more distant. In aconjugately-equalized system as the one described, the behavior iseffectively resistance-controlled over most of the operating range. Inthe example cited above the system will be resistive from about 20 Hz toabout 80 Hz which is the entire operating range in many applications. Insuch a system, the acoustic output is in-phase with the electrical inputso no additional delay is present.

The present invention represents a significantly powerful techniquebecause it turns the design process on its head.

Usually one would:

a. Choose the box size

b. Choose a desired lower frequency limit

c. Try to find (or design) a driver which will get you there.

Usually, and especially for a small box and a low cutoff frequency, thedriver has to have a loose suspension and a high moving-mass. This isthe only way the resonance can be held to a low frequency.Unfortunately, this combination of attributes leads directly to poorelectro acoustic conversion efficiency and poor acceleration hence poorrendering of the attack of bass sounds. These are the well knowndeficiencies of so-called “acoustic suspension” woofer systems. Thetradeoffs for remedying this in a conventional system are unyielding.

With the present invention, however, one would:

a. Optimize the driver with respect to motor strength, low mass and highsuspension stability;

b. Choose the box size;

c. Choose the lower frequency limit;

d. Measure the Ftc, Qtc of the speaker in the box; and

e. Set up the equalizer accordingly.

The use of equalization increases the power demand below Fz compared toFz and above. This is not the liability it might seem. This is becausethe efficiency due to the high Ftc is substantially increased so thestarting point for looking at the power demand is much lower. Given thestatistics of low-frequency content in music and movies, the averagepower required for a woofer system employing the present invention isusually less than for a conventional one.

The methodology described above perfects the frequency response of thewoofers for small signals. It should be noted that woofers are generallycalled upon to reproduce large signals as there is often high acousticpower at low frequencies in music. Regardless of the method used toachieve flat frequency response, there is still the consideration thatthe required axial displacement of the diaphragms of the woofers isinversely proportional to the square of the frequency. For example, toproduce the same sound pressure at 25 Hz as is produced at 50 Hz, thediaphragms of the woofers must travel 4 times as far. Normally thisleads to a situation where the woofers can reach their excursion limitsat very low frequencies. In the instant invention the equalization isalready present and it can be conveniently modified on a dynamic basisto prevent said excessive diaphragm excursion.

As noted above, the use of the 2 integrator state-variable filtertopology allows this control. What is required at high amplitudes is tochange the ratio of Fz/Fp independently of the other three parameters,Fz, Qz and Qp. This can be accomplished by introducing a multipliercircuit in the feedback path for the frequency ratio and the poledamping as shown in FIGS. 6 and 7. The equations for this implementationare as follows: Assume the multiplier solves (((+x)−(−x)×(+y)−(−y))/10),i.e. the product of the differential inputs divided by 10. The controlcoefficient is (10/(+x)−(−x))=V.V=(10/(+x)−(−x))=(Fz/Fp)²

-   -   K=added ping coefficient        Qp=(KsqrtV)/(V+K)        The reason for the presence of K is that without it, V will        control the square of the frequency ratio, but will control Qp        linearly. This could be solved by adding another multiplier but        would be an unnecessarily complicated solution. Instead, adding        a fixed damping term, K will cause Qp to remain constant within        about 10 percent. The practical consequence of this is less than        1 dB in amplitude at the dynamically adjusted cutoff frequency        and is not audible in practice.

It remains to control V. For this purpose, the audio signal is passedthrough a second order low-pass filter which has the same frequency asFp unmodified, (i.e. Fz/Fp is at the static maximum value, see below)and the same Q as Qp. The output of this filter varies with frequencythe same as the diaphragm excursion of the woofers, so it effectively isan analog of the diaphragm motion. This voltage is then scaled andpeak-detected above a predetermined threshold and applied to thedifferential x input of the mutiplier. As the system attempts tooverdrive the woofers, Fp will be shifted upward just far enough toprevent frequencies below it from causing excessive excursion. Becausethis process is dynamic, and is only applied to the extent required toprevent the overload there is almost no adverse audible effect.

It should be noted that the control law for Fp is dB/dB so that thecontrol sidechain can be arranged as either feed-forward or feed-back.Many methods exist for peak-detection and detection threshold settingand the details are left to one skilled in the art of analog circuitdesign.

Example

The following assumptions are made in the present example:

1. The total box volume is 90 liters (3.18 cubic feet)

2. Two woofers are mounted identically on opposite sides of the box

3. The woofer nominal diameter is 300 mm (12″)

4. The woofers are identical

5. The lower cutoff frequency is to be 20 Hz

The driver is then optimized:

-   -   1. A low moving mass is chosen consistent with adequate        structural strength in the diaphragm. A value of 45 grams is        reasonable based on experience.    -   2. A mechanical compliance (Cm) is chosen which will give good        stability to the suspension of the diaphragm. A value of 4.59E-4        meters/Newton is reasonable based on experience. For a 12″        driver this equates to a compliance equivalent volume (Vas)        equal to Cm×ρ₀×c²×Sd² where ρ₀ is the density of air, usually        taken to be 1.18 kg/cubic meter, c is the velocity of sound        usually taken to be 345.45 m/s and Sd is the surface area of the        diaphragm which for a 300 mm nominal driver is about 0.045        square meters. Vas represents the volume of air whose        compressibility is equal to the mechanical compliance. Vas in        this case is equal to 131 liters.    -   3. The mass and compliance chosen above will result in a        fundamental resonance frequency of 35 Hz.    -   4. The total damping of the driver resonant system is        established by the motor strength expressed as the product of B,        flux density in the gap and L, the length of voice-coil        conductor in the gap. Actually there are two sources of damping,        the pure mechanical losses of the moving system (Qm) and the        force exerted by the motor. In a well optimized driver the motor        damping completely dominates. The motor damping alone is called        Qe, the electrical Q. It is established by the relationship        Qe=DCM(B×L)²×2πFs×Cm). Since Cm and Fs have already been        determined, the Qe depends on DCR, the voice coil resistance and        B×L.    -   5. Motor design in loudspeakers is superficially simple but        actually requires considerable experience, and/or the use of        assistive software which is commercially available. Those        skilled in the art will recognize that a motor with a B×L        product of about 20 Tesla meters and a DCR of 7 Ohms is quite        feasible. These values, along with the determinations made above        will yield Qe=0.173.    -   6. In the woofer system of the present example the drivers are        connected electrically in parallel. The result is that the DCR        drops in half and B×L remains unchanged. However, total force        developed by the two motors is equal to B×L×I, where I is the        current through the voice coil. For a fixed applied voltage, I        doubles because DCR dropped in half. Therefore the total force        is double.    -   7. To summarize the resulting driver parameters:        -   a. Nominal diameter=300 mm        -   b. DCR=7 Ohms, 3.5 Ohms for 2 drivers in parallel        -   c. B×L=20 Tesla meters        -   d. Fs=35 Hz        -   e. Qe=0.173, and assuming Qm=5, then        -   f. Qt=0.167. Qt is the parallel combination of Qe and Qm.        -   g. Vas=262 liters for 2 drivers            There is now sufficient information to design the equalizer.

It is well known to those skilled in the art, that the parameters of thedrivers as modified by the enclosure is easily calculated. The requiredcomputational inputs are:

1. The box volume

2. The Vas of the intended drivers

3. The Qt of the intended drivers

-   The compliance ratio, α (alpha) is equal to Vas/Vbox. In this case    α=262/90=2.911-   Then the term sqrt(α+1) is found equal to 1.978 (2 for practical    purposes).

This means that when the two optimized drivers are mounted in the 90liter box, or separately in 45 liter boxes as shown in FIG. 1, the newvalues Ftc and Qtc will appear. These are the modified values of thefundamental resonance due to the stiffness of the air in the box. Theyare found by multiplying Fs and Qt by 1.978. Thus, Qtc=0.334 and Ftc=70Hz.

Taken by themselves, these are unattractive parameters for a completesystem. The Ftc is too high and in this case the Qtc is too low. Theresult will be deficient low frequency response.

Referring to the equalizer circuit of FIG. 4A, the design objectives aremet as follows:

-   -   1. Qz is set equal to Qtc=0.334. Thus R8 is set for 3.34 KΩ.    -   2. Fz is set equal to Ftc=70 Hz. Thus, assuming C1 and C2 are        arbitrarily chosen to be 100 nanoFarads (nF), then R2 and R3        must equal 22.74 KΩ.    -   3. The values indicated for R8, C1, C2, R2 and R3 cancel the        driver characteristic.    -   4. The new low frequency pole is set according to the system        design objectives given. For a maximally flat response with a        lower limit of 20 Hz, Fpole=20 Hz and Qpole=0.71, a so-called        Butterworth alignment.    -   5. Thus R5=(70/20)²×10 KΩ=120.2 KΩ, and R11=0.71(70/20)×10        KΩ=24.8 KΩ.    -   6. The total resulting boost between frequencies >>70 Hz and <20        Hz, in dB, will be equal to 40 log (70/20)=21.7 dB. This        corresponds to a power ratio of 147:1. It can be seen that this        approach requires significant power and the design details to        handle such power reliably. The means to do this will be well        known to those skilled in the art.

Referring to FIGS. 6 and 7, the reconfiguration for dynamic adjustmentof the Fz/Fp parameter is shown. For purposes of illustration consider aslightly different set of unequalized woofer parameters and a slightlydifferent design objective:

-   -   1. Qz is set equal to Qtc=0.50. Thus R8 is set for 5.00 KΩ    -   2. Fz is set equal to Ftc=60 Hz. Thus, assuming C1 and C2 are        arbitrarily chosen to be 100 nF, R2 and R3 must equal 26.5 KΩ.    -   3. The values indicated for R8, C1, C2, R2 and R3 cancel the        driver characteristic.    -   4. The new low frequency pole is set according to the system        design objectives; in this case Fpole=20 Hz and Qpole=1.    -   5. Thus coefficient K is calculated as described earlier to be        about 4.5, thus R11=45 KΩ.    -   6. The equalization set voltage is adjusted for Fz/Fp=60/20=3.        This requires 1.11 Volt at the x(−) input of the multiplier with        respect to the x(+) input.    -   7. The low-pass filter in the control chain is set the same as        the system objective; Fp=20 Hz, Qp=1. Thus C3 and C4=795 nF and        R16=10 KΩ.

The full-wave negative peak detector indicated in FIGS. 6 and 7 mustperform the detection only after the input to it has exceeded a certainthreshold. This is related to the voice-coil voltage at which thewoofers reach their maximum allowable excursion at Fp minimum (i.e.Fz/Fp maximum). This requires the voltage gain of the power amplifier tobe known. This amplifier is not shown but is connected between theoutput of FIG. 7 and the woofers. For example:

-   -   1. Assume the maximum input voltage to the woofers, which are        connected in parallel so the voltage is the same on both of        them, is 40 Volts rms which is equal to 56.56 Volts peak.    -   2. Assume the power amplifier voltage gain is 20. This means        that when the voltage at the output of FIG. 7 reaches 2V rms at        Fp minimum, the woofers will be at their mechanical limit.    -   3. The low-pass filter, U7, has a gain of 2 in the passband, so        2V rms at the output of FIG. 7 will cause 4V rms at the input to        the negative peak detector. The peak value of 4V rms is 5.656V        which is the threshold of operation. Signals larger than this        will cause Fp to rise, thus reducing the total boost and        preventing excessive excursion of the woofers. The low-pass        filter, U7, conditions the detector input according to the        excursion vs frequency charactersitic of the woofers.

FIG. 8 shows the various relationships for the adaptive embodiment ofthe equalizer.

-   -   1. The voltage controlled filter characteristic describes how        the filter changes with changes in ((x(+)−x(−)), the        differential control input.    -   2. The unequalized woofer characteristic is to be corrected by        the filter by setting Fz and Qz of the filter equal to Ftc and        Qtc of the woofer, respectively.    -   3. The woofer diaphragm excursion vs frequency relationship        shows the inverse square relationship for constant sound        pressure.    -   4. The dynamically equalized response shows that above the        threshold of detection, the reduction of Fz/Fp causes a        reduction in the output below the inflection point which        eliminated excessive excursion of the woofer diaphragms.

What is claimed is:
 1. A system for optimizing low frequency audioresponse, comprising: one or more low frequency transducers electricallyconnected to a power amplifier and an audio input, said one or more lowfrequency transducers emanating low frequency audio signals into anenclosed volume; and an equalizer placed between said power amplifierand said audio input, wherein said equalizer is adapted to (a)characterize the resonant frequency (Fs) and amplitude (Q) of thehigh-pass complex pole of said one or more low frequency transducersemanating low frequency audio signals into said enclosed volume, (b)cancel the complex pole of said one or more low frequency transducers,and (c) establish a new variable complex pole for establishing a lowercut off frequency below which the output generated by low frequencytransducers diminishes.
 2. The system of claim 1, wherein said one ormore are mounted in a closed cabinet.
 3. The system of claim 1, whereinsaid one or more transducers are mounted in separate closed cabinets. 4.The system of claim 1, wherein said variable complex pole iselectrically controllable.
 5. The system of claim 4, wherein saidelectrical control is determined by an electrical analog of thediaphragm excursion of said one or more tranducers.
 6. The system ofclaim 1, wherein the moving mass of the one or more transducers is notincreased.
 7. The system of claim 1, wherein the stiffness of the one ormore transducers is not decreased.
 8. The system of claim 1, wherein theequalizer comprises two integrators.
 9. The system of claim 1, whereinthe enclosed volume comprises a volume of air with stiffness, and theresonant frequency and amplitude are raised in value due to thestiffness of the air in the volume.